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Oberseminar WiSe 2007/08 Abstract to the talk by K. Wendland, Augsburg

On K3 surfaces and beyond &mdash from a geometer's and a conformal field theorist's point of view

The moduli space of Einstein metrics on K3 is well-known to algebraic and differential geometers. Physicists have introduced the notion of conformal field theories (CFTs) associated to K3, and the moduli space of these objects is also well understood. It can be interpreted as a generalisation of the moduli space of Einstein metrics on K3, which allows us to introduce this space without having to use background knowledge from CFT. However, just as no smooth Einstein metrics on K3 are known explicitly, the explicit construction of CFTs associated to K3 in general remains an open problem.

We use classical results by Shioda and Inose to explicitly construct a family of CFTs which are associated to a family of smooth algebraic K3 surfaces. We also explain how results on CFTs associated to K3 can be used to address CFTs associated to special higher dimensional Calabi-Yau varieties.